Hi Snuffy,
I can't speak for the Little Red Deer or Fallen Timber specifically; however, I've spent some time on the brown trout streams near RMH (Prairie, Stauffer, South Raven). I'll try to answer the first two of your questions and hopefully somebody with more experience on the water valley area can correct me if I am wrong and fill in the rest.
1) While I believe that a several years ago the Little Red and Fallen Timber were subjected to a series of drought and flood years, I believe that they hold a good population of browns today. It often takes the right conditions (light, temperature, hatches, etc.) to see what these rivers can really produce. I've fished the streams mentioned above and had days ranging from marginal to phenomenal. On the days where it seems that you just can't buy a riser, I often find stripping streamers (wooly buggers being a favorite) near undercut banks and log jams to be the most effective.
2) I fish the gravel bottom sections more than the mud-bottom sections but that is just my preference. I wouldn't even try to argue that the gravel sections are better as I've seen and heard of some great fish coming out of the slower, mud-bottomed sections.
Don't get discouraged as these can be incredible streams to fish!
Brandon